Variability and uncertainty of biokinetic model parameters: the discrete empirical Bayes approximation

In the Bayesian approach to internal dosimetry, uncertainty and variability of biokinetic model parameters need to be taken into account. The discrete empirical Bayes approximation replaces integration over biokinetic model parameters by discrete summation in the evaluation of Bayesian posterior averages using Bayes theorem. The discrete choices of parameters are taken as best-fit point determinations of model parameters for a study subpopulation with extensive data. A simple heuristic model is constructed to numerically and theoretically study this approximation. The heuristic example is the measurement of heights of a group of people, say from a photograph where measurement uncertainty is significant. A comparison is made of posterior mean and standard deviation of height after a measurement, (i) using the exact prior describing the distribution of true height in the population and (ii) using the approximate discrete empirical Bayes prior obtained from measurements of some study subpopulation.